iPTF methods: How Green’s identity and FEM solver can be used for acoustic inverse methods

Invited paper

LVA - INSA Lyon

Tuesday 2 june, 2015, 09:40 - 10:00

0.8 Rome (118)

Abstract:

Green’s identity is a well-known mathematical tool usually used to solve
acoustic problems. If two functions are twice continuously differentiable, an
integral over a volume can be replaced by an integral over the surfaces of the
volume. Mostly, one of these functions is the acoustic pressure but the other
one is completely arbitrary. The possibilities given by this arbitrary choice
are numerous.
In the present paper, the powerful capabilities of the Green’s identity will
be illustrated on a 3D acoustic problem consisting in an oil pan radiating in
a semi-infinite medium. The radiated field obtained by Infinite Element
(considered here as a reference) will be compared to the solution provided by
Green’s identity using a finite virtual volume surrounding the vibrating
surface. Thanks to Green’s identity, the choice of the boundary conditions of
this virtual volume is arbitrary. The cases of homogeneous (Neumann) and mixed
(Neumann and Dirichlet) boundary conditions will be presented.
Finally, it will be shown how Green’s identity and FEM solver can be used as
acoustic inverse method. The so-called “homogeneous iPTF” (inverse Patch
Transfer Functions with homogeneous BC) and “mixed iPTF” (inverse Patch
Transfer Functions with mixed BC) will be presented and experimentally applied
on the case of the oil pan. Velocity, pressure and intensity fields
reconstructed by the inverse methods will be compared to direct measurements.